In this paper, the relation among the polynomial in several elements and the period and linear complexity of the clock controlled sequences over the finite field GF(q)(q=p^a，P≥2 is a prime number, a≥1 is a positive integer number)is discussed. When the n-pry polynomial g(x₁,x₂,…,x_n) ∈GF(q)[x₁,x₂,… ,x_n] is a polynomial of degree 1, we give the necessary and sufficient condition that the clock controlled sequences get to the maximum period and the maximum linear complexity.